Speaker(s)Pierre Colmez (Institut de Mathématiques de Jussieu)Description No Description

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The algebraic closure of the field ${\bf Q}_p$ of $p$-adic number is infinite dimensional over ${\bf Q}_p$, hence its completion ${\bf C}_p$ is also infinite dimensional. I will describe objects that can be thought of as finite dimensional vector spaces over ${\bf C}_p$ up to finite dimensional ${\bf Q}_p$-vector spaces and explain what kind of properties they have. I will end up with some recent applications.